Question

The hypotenuse of a right triangle is 6 m more than the twice of the shortest side. If the third side is $2m$ less than the hypotenuse, find the sides of the triangle.

Answer 1

Let the shortest side be $x.$
Then hypotenuse $=2x+6$
Third side $=2x+6-2=2x+4$
According to Pythagoras theorem,
$A{B}^2=C{B}^2+A{C}^2$
$(2x+6{)}^2=x^2+(2x+4{)}^2$
$4x^2+24x+36=x^2+4x^2+16x+16$
$x^2-8x-20=0$
$(x-10)(x+2)=0$
$x-10=0orx+2=0$
$x=10$ or $x=-2$
$x$ cannot be negative.
So shortest side is $10m.$

Hypotenuse $=2x+6$
$=2\times 10+6$
$=20+6$
$=26m$
Third side $=2x+4$
$==2\times 10+4$
$=20+4$
$=24m$

Hence the shortest side, hypotenuse and third side of the triangle are $10m,26m$ and $24m$ respectively.